CBSE · Class 6-12

Class 10 · Mathematics (Standard)

Unit 3 · Class 10Mathematics (Standard)

Pair of Linear Equations in Two Variables

Graphical and algebraic methods (substitution, elimination) to solve two linear equations in two variables.

Lessons

5 concepts

1
Graphical Interpretation
Each equation $a_1x + b_1y + c_1 = 0$ represents a straight line. Two lines can (i) intersect at one point — unique solution (consistent, independent), (ii) be coincident — infinitely many solutions (consistent, dependen…
2
Substitution Method
Solve one equation for one variable, substitute into the other, and solve. E.g. from $x - y = -1$ we get $x = y - 1$ ; put in $3x - 5y = -1$ : $3(y-1) - 5y = -1 \Rightarrow -2y = 2 \Rightarrow y = -1, x = -2$ .
3
Elimination Method
Multiply the equations by suitable numbers so that a variable's coefficients match, then add or subtract to eliminate that variable. Solve the resulting one-variable equation, then back-substitute for the other.
4
Reducing to Linear Form
Some non-linear systems can be linearised by substitution. E.g. $\dfrac{2}{x} + \dfrac{3}{y} = 13,\; \dfrac{5}{x} - \dfrac{4}{y} = -2$ becomes linear in $u = 1/x, v = 1/y$ .
5
Word-Problem Setup
Translate each condition into an equation. Common contexts: ages, digits of numbers, mixtures, speed–distance–time, prices/quantities. Always define the variables clearly at the start.

Skills to practise

Skill · medium

Pair of Linear Equations in Two Variables — Practice